Hi everyone, the other day I wrote down some modifications to a NLP model and after expending some time doing some calculations (long story), I found out that I had to solve this limit:
So, I didn’t think too much, I opened Mathcad, wrote the equation and got the following solution:
I was very pleased at that moment because I had the solution, but then I thought, what would had happened if I didn’t have a computer?, what would had happened if I was writing my model in a dessert island after a shipwreck?. And then I got worried, I found out that I depend on computers :-(.
After crying for a few hours, I decided to solve this limit without Mathcad, so I opened Mathematica and wrote the same limit (jajaja, just kidding). I started analysing this function, so I draw it in a paper and got something like this:
As we can see, we find symmetry respect on zero and that’s quite encouraging.
Then I remembered that if we have something like, with
, then we have:
Where zj is the root j of Q(k).
So I decided to use this property to solve my problem:
So,
Which is kind of similar to the solution we found at the beginning!.
After that, I remembered that my function was symmetric so,
And so my limit was at one step to be solved! I just only needed to divide by two and all my distresses would pass away!, I happily got my solution:
Now I can sleep at night :-)
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